It's been 6 years or so since I shot a 3 gun match so I don't know what they are like now. Don't worry about shooting well or fast. For your first few matches just worry about being safe and learning the flow of things.
Likely you won't need more than 3 mags for the pistol and rifle for a single stage. The range will probably be a cold range so you will not have any loaded guns until you are on the line and ready to shoot. One mistake I made early on was to not have a mag pouch for my starting mag when I was between stages.
The stages we shot were mostly 25 yards and under, however it was not uncommon to have a few AR targets out to 300. Make sure you know your bullet drop for extended ranges.
You might need some slugs for the shotgun and you will need to know the POA/POI out to 100 yards. Try to get the lightest slug loads you can find, but make sure you test them before. Shotguns can be very finicky on what they will cycle. I don't think we ever shot buck shot. Reloading the shotgun is the most awkward part of the whole day. I would say if you are going to practice anything before hand, watch some videos online and practice reloading the shotgun. Be prepared to pinch your thumb and get your thumb nail caught on the shell lifter. If your wife has fancy nails this will be the part she doesn't like the most.
Have a plan for what you are going to do with all of your gear while you are not shooting. You will spend 1-2 minutes shooting and then 30ish minutes watching other people shoot before moving to the next stage. This is why wagons and jogging strollers are so popular in 3-gun. One range I use to shoot at was fairly large so people would bring SXS's with gun racks on them. One guy had vertical racks mounted to the outside of the cage on a YJ. Also mag loading tools are well worth the money.
As for a belt, I ran a normal gun type belt for a long time before I switched to a Double Alpha inner/outer type. The only advantage to an inner/outer style I could see at this point is that it would be easy to swap between you and your wife if you got two inner belts, assuming you both have similar size waists.